Abstract Algebra: Week 6 homework help

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Problem 68 solution is incorrect. The reason I'm wrong is that my solution assumes Z4 is a field, but, it's not and that means there can be solutions not covered by my method. You can find 8 units in Z4[i] as it happens.

jamescook
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Love that method at the end for finding alpha inverse

hxc
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Is there any structures such that those are non commutative in addition and distributive or non distributive in scalar multiplication and associative and it's infinite dimensional 🤔

jellyfrancis